相关论文: Existence and Optimality of $w$-Non-adjacent Forms…
We introduce a family of maps generating continued fractions where the digit $1$ in the numerator is replaced cyclically by some given non-negative integers $(N_1,\ldots,N_m)$. We prove the convergence of the given algorithm, and study the…
We examine a unique construction of the real numbers which proceeds directly from the integers using approximately linear-endomorphisms with finite error, called near-endomorphisms. In this paper, we show that the set of near-endomorphisms…
The problem of designing physical-layer network coding (PNC) schemes via nested lattices is considered. Building on the compute-and-forward (C&F) relaying strategy of Nazer and Gastpar, who demonstrated its asymptotic gain using…
We show that there are four chiral ${\cal W}$-algebra extensions of $\mathfrak{so}(2,3)$ algebra and construct them explicitly. We do this by a simple identification of each of the inequivalent embeddings of a copy of…
This work presents an accurate numerical study of the electrostatics of systems formed by individual nanostructure mounted on support substrate tip, a theoretical prototype for applications in field electron emission or for construction of…
Lie-theoretic structures of type $E_8$ (e.g., Lie groups and algebras, Hecke algebras and Kazhdan-Lusztig cells, ...) are considered to serve as a `gold standard' when it comes to judging the effectiveness of a general algorithm for solving…
We investigate the Hausdorff dimension of level sets defined by digit growth rates in $\theta$-expansions, a generalization of regular continued fractions. For any $\alpha \geq 0$, we prove that the set \[ E_\theta(\alpha) = \left\{ x \in…
Let $(\alpha,\mathcal{N}_{\alpha})$ and $(\beta,\mathcal{N}_{\beta})$ be two canonical number systems for an imaginary quadratic number field $K$ such that $\alpha$ and $\beta$ are multiplicatively independent. We provide an effective lower…
Computing a basis for the exponent lattice of algebraic numbers is a basic problem in the field of computational number theory with applications to many other areas. The main cost of a well-known algorithm…
The digits of the Pierce expansion satisfy the law of large numbers. It is known that the Hausdorff dimension of the set of exceptions to the law of large numbers is 1. We provide an elementary proof of this fact by adapting Jun Wu's…
In order to increase the accuracy of the linearized augmented plane wave method (LAPW) we present a new approach where the plane wave basis function is augmented by two different atomic radial components constructed at two different…
We investigate the stability of low-friction sliding of nanocrystal with rectangular atomic arrangement on rectangular lattices, for which analytical results can be obtained. We find that several incommensurate periodic orbits exist and are…
A detailed account of the implementation of equations of the Relativistic Density Functional Theory (RDFT) using basis sets of APW/LAPW type with flexible extensions provided by local orbitals is given. Earlier discoveries of the importance…
The main purpose of this paper is to study the arithmetical properties of values \(\sum_{m=0}^{\infty} \beta^{-w(m)}\), where \(\beta\) is a fixed Pisot or Salem number and \(w(m)\) (\(m=0,1,\ldots\)) are distinct sequences of nonnegative…
This paper explores two techniques on a family of hyperelliptic curves that have been proposed to accelerate computation of scalar multiplication for hyperelliptic curve cryptosystems. In elliptic curve cryptosystems, it is known that…
Suppose that $\Omega$ is a complex lattice that is closed under complex conjugation and that $I$ is a small real interval, and that $D$ is a disc in $ \mathbb{C}$. Then the restriction $\wp|_D$ is definable in the structure…
The coexistence of different wireless communication systems such as LTE and Wi-Fi by sharing the unlicensed band is well studied in the literature. In these studies, various methods are proposed to support the coexistence of systems,…
A number of constructions in function field arithmetic involve extensions from linear objects using digit expansions. This technique is described here as a method of constructing orthonormal bases in spaces of continuous functions. We…
A fundamental challenge within the metric theory of continued fractions involves quantifying sets of real numbers, when represented using continued fractions, exhibit partial quotients that grow at specific rates. For any positive function…
We report findings from several ab-initio, self-consistent calculations of electronic and transport properties of wurtzite aluminum nitride. Our calculations utilized a local density approximation (LDA) potential and the linear combination…